Using the Abel–Prym map and the polyhedral structure of the symmetric product, we can naturally assign a volume to the cells of the Prym variety.
Theorem REF  therefore describes the volume of the Prym variety as a weighted sum
over all the relative spanning trees. This result is known as the tropical Prym–Kirchhoff matrix-tree theorem.
In the special case where all edge lengths are 1, the formula was known prior to the discovery of tropical Prym varieties in the language of critical groups (see [1]}).

